Should RNA-seq data (almost) always be assembled first into contigs before analyzing? From what I can see, not all published transcriptome studies assemble the reads before proceeding onto expression level analysis.

My understanding is that assembling into contigs will enable better ORF/gene detection, but are there analyses that can be done before assembling?

There is a draft genome for this organism, but it's only on its first release. I worry that by aligning the reads to a maybe not-so-accurate genome can cause me to lose out on useful information in the transcriptome?

Do both. Even with the draft genome you would get an idea of what your data looks like projected against the genome. If this is a eukaryotic genome then you are likely to use Trinity to assemble the transcriptome. This could require significant amount of compute resources.